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A  Study  of  the  Transference  Numbers  of 
Sulfuric  Acid  and  the  Influence  of 
Gelatin  on  the  Transference 
Numbers  by  the  Concen- 
tration Cell  Method 


A  THESIS 


SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  OF  THE 
UNIVERSITY  OF  MICHIGAN  IN  PARTIAL  FULFILLMENT  OF 
THE  REQUIREMENTS  FOR  THE  DEGREE  OF  DOCTOR 
OF  PHILOSOPHY 

June  1921 


By 
Wesley  George  I  France 


EASTON,  PA. 
ESCHENBACH  PRINTING  COMPANY 

JUNE  1921 


A  Study  of  the  Transference  Numbers  of 
Sulfuric  Acid  and  the  Influence  of 
Gelatin  on  the  Transference 
Numbers  by  the  Concen- 
tration Cell  Method 


A  THESIS 


SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  OF  THE 

UNIVERSITY  OF  MICHIGAN  IN  PARTIAL  FULFILLMENT  OF 

THE  REQUIREMENTS  FOR  THE  DEGREE  OF  DOCTOR 

OF  PHILOSOPHY 

June  1921 


By 


Wesley  George  France 
tf 


EASTON,  PA. 

ESCHENBACH  PRINTING  COMPANY 
JUNE  1921 


F/ 


«*CHANGfc 


TABLE  OF  CONTENTS. 


I.     Introduction 5 

II.     Historical ' 5 

III.  Theoretical 7 

IV.  Apparatus  and  Materials 9 

V.     Arrangement  of  Cells  and  Method  of  Procedure 10 

VI.    Experimental  Results  with  Sulfuric  Acid 11 

VII.    Experimental  Results  with  Sulfuric  Acid  Containing  Gelatin 17 

VIII.    Summary 27 


ACKNOWLEDGMENT. 

The  author  wishes  to  express  his  appreciation  for  the  most  valuable 
aid  and  advice  given  during  the  progress  of  this  work  by  Doctor  Alfred  L. 
Ferguson,  at  whose  suggestion  and  under  whose  direction  it  was  carried  out. 

It  is  with  much  pleasure  that  acknowledgment  is  made  to  Professor 
S.  Lawrence  Bigelow,  for  his  many  valuable  criticisms. 


A  STUDY  OF  THE  TRANSFERENCE  NUMBERS   OF   SULFURIC 
ACID  AND  THE  INFLUENCE  OF  GELATIN  ON  THE 
TRANSFERENCE  NUMBERS  BY  THE  CON- 
CENTRATION CELL  METHOD 

INTRODUCTION. 

Three  methods  have  been  used  for  the  determination  of  transference 
numbers ;  the  analytical,  the  moving  boundary,  and  the  concentration  cell. 
The  oldest  and  most  generally  used  is  the  analytical  discovered  by  W. 
Hittorf.  The  moving  boundary  method  was  first  described  by  O.  Lodge 
and  has  been  developed  and  used  by  R.  B.  Dension  and  B.  D.  Steele. 
The  concentration  cell  method  has  been  used  in  only  a  few  cases  and  with 
varying  success;  its  reliability  for  uni-univalent  electrolytes,  however, 
has  been  demonstrated  in  this  laboratory. 

The  present  investigation  is  an  application  of  the  concentration  cell 
method  to  the  determination  of  the  transference  numbers  of  a  uni-bivalent 
electrolyte.  In  the  first  part  of  the  work  the  electrolyte  used  was  sulfuric 
acid,  and  in  the  second  part  sulfuric  acid  plus  definite  quantities  of  gelatin. 

Historical.1 

The  first  investigator  to  develop  a  successful  method  for  the  determina- 
tion of  transference  numbers  was  W.  Hittorf.  (Pogg.  Ann.,  89, 177  (1853)). 
In  this  work  an  electrolytic  cell  was  used  in  which  a  strip  of  silver  always 
served  as  cathode  and  a  metal  which  corresponded  to  the  metal  ion  of  the 
electrolyte  as  anode.  The  transference  numbers  were  calculated  from  the 
change  in  concentration  around  the  anode  which  resulted  from  the  passage 
of  a  measured  quantity  of  electricity.  This  method  was  improved  in 
many  respects  by  him  during  the  next  few  years  and,  as  finally  used,  was 
the  same  in  all  essentials  as  the  present  Hittorf  method. 

Hittorf  is  given  credit  for  the  origination  of  this  method  for  the  determi- 
nation of  transference  numbers,  although  there  were  several  earlier  in- 
vestigations on  the  changes  which  take  place  about  the  electrodes  during 
electrolysis.  As  early  as  1814  R.  Porrett  (Abst.  Phil.  Trans.,  1,  510) 
investigated  the  movement  of  iron  and  potassium  ions  when  a  solution  of 
ferrocyanic  acid  was  electrolyzed.  M.  Faraday  (Phil.,  Trans.  123,  682, 
525,  (1833))  studied  the  relative  changes  in  acidity  produced  by  electroly- 
sis in  equivalent  solutions  of  NaOH  and  H2SO4.  J.  F.  Daniell  (Phil.  Trans., 
129,  97  (1839) ;  130,  209  (1840)) ;  J.  F.  Daniell  and  W.  A.  Miller  (ibid.,  134, 
1  (1844));  and  M.  Pouillet  (Comptes  rendus,  20,  1  sem.  1544  (1845)) 
conducted  similar  investigations  and  were  able  to  calculate  from  their 
1  For  a  complete  abstract  and  bibliography  of  Transference  Numbers  up  to  and 
including  the  work  of  1905,  see  J.  W.  MacBain.  (/.  Wash.  Acad.  Sci.,  9,  1.) 


6 

results  migration  ratios.  The  values  so  obtained  are  approximations 
only,  since  strict  quantitative  procedures  were  not  employed. 

The  moving  boundary  or  direct  method  for  the  measurement  of  the 
migration  velocity  of  ions  was  first  described  by  O.  Lodge  (Brit.  Assoc. 
Rep.,  389  (1886)).  Two  cups  with  suitable  electrodes  and  electrolytes 
were  connected  by  means  of  a  horizontal  siphon  filled  with  gelatin  which 
contained  phenolphthalein  or  some  salt.  When  a  current  was  passed 
through  the  apparatus  the  diffusion  of  the  ions  caused  either  a  color 
change  or  a  precipitation  in  the  gelatin.  As  the  diffusion  progressed  the 
color  change  or  precipitation  produced  a  sharp  boundary.  From  the 
velocity  of  movement  of  this  boundary  the  transference  numbers  were 
calculated. 

The  concentration  cell  method  was  first  suggested  by  von  Helmholtz 
(Ges.  Abh.,  I  840,  II  979) .  By  the  use  of  thermodynamic  principles  together 
with  the  phenomenon  of  vapor  pressure,  he  showed  that  transference 
numbers  can  be  expressed  by  the  ratio  of  the  potential  of  a  concentration 
cell  with  diffusion  to  that  of  a  concentration  cell  without  diffusion.  This 
method  appears  open  to  fewer  objections  than  either  the  analytical  or 
moving  boundary  methods.  It  has,  however,  been  used  less  extensively 
than  the  others.  This  is  undoubtedly  due  to  the  difficulties  encountered 
in  the  construction  of  suitable  electrodes. 

The  method  was  first  experimentally  tested  by  J.  Moser  (Wien.  Sit- 
zungsber.,  92,  Abth.  II,  652  (1885).  He  obtained  for  the  transference 
numbers  of  the  anions  of  ZnSC>4  and  ZnCl2  .64  and  .71  which  agreed  well 
with  the  values,  .636  and  .700,  obtained  by  Hittorf . 

No  further  use  of  the  method  was  made  until  1898.  At  this  time  G. 
Kummell  (Wied.  Ann.,  64,  655)  determined  the  transference  numbers  of 
ZnCl2,  ZnSO4,  CdCl2,  and  CdSO4.  These  results  did  not  agree  well  with 
those  obtained  by  Hittorf. 

The  same  year  D.  Mclntosh  (J.  Phys.  Chem.,  2,  273)  made  an  investi- 
gation of  the  method.  The  transference  number  of  the  hydrogen  ion  in 
H2SO4,  HC1,  HBr,  HI,  and  H2C2O4  was  determined.  In  most  of  the  work 
cells  of  the  types 

PtH— HC1  ci— HC1  c2— PtH 
and 

PtH— HC1  cr-  HgCl— Hg— HgCl— HC1  C2— PtH 
were  used.     However  some  work  was  done  with  cells  of  the  types 

Ptci— HC1  ci— HC1  CT-  Pta 
and 

PtCi— HC1  ci— PtH— HC1  c2— Pta. 

As  a  result  of  his  investigation,  Mclntosh  was  led  to  conclude  that  the 
method  was  not  suitable  for  use  with  gas  cells.  This  conclusion  appears 
to  be  founded  on  two  facts ;  the  failure  of  the  cells  of  the  first  type  to  give 


values  in  agreement  with  those  of  the  second,  and  the  lack  of  agreement 
between  the  velocity  which  he  obtained  for  the  hydrogen  ion  and  that 
calculated  from  the  conductivity  data  of  Kohlrausch.  That  this  con- 
clusion was  not  entirely  justified  is  evident  from  a  consideration  of  the 
rather  wide  variation  between  the  cells  intended  to  be  duplicates.  The 
variation  in  some  cases  is  .0015  volt.  There  also  appears  to  have  been 
no  effort  made  to  maintain  the  cells  at  a  constant  temperature.  From 
the  results  obtained  later,  by  other  investigators,  it  appears  that  his  diffi- 
culty was  not  inherent  in  the  method,  but  in  the  construction  of  the 
electrodes. 

The  same  method  was  employed  by  D.  A.  Maclnness  and  K.  Parker 
in  their  determination  of  the  transference  numbers  of  KC1  (/.  A.  C.  S., 
37,  1445  (1915)).  They  used  potassium  amalgam  and  silver  chloride 
electrodes  and  obtained  satisfactory  results. 

The  most  recent  application  of  the  method  was  in  the  investigation  of 
the  transference  numbers  of  HC1  by  A.  I,.  Ferguson  (J.  Phys.  Chem.,  20, 
326  (1916)).  Hydrogen  and  calomel  electrodes  wrere  used  the  tempera- 
ture was  maintained  at  25  °  C.  The  potentials  were  measured  to  .00001  volt 
and  the  maximum  variation  of  the  cells  was  about  .0001  volt.  The  trans- 
ference numbers  obtained  agreed  very  well  among  themselves  and  also 
with  the  best  accepted  values  of  other  investigators.  This  work  resulted 
in  the  establishment  of  the  value  and  reliability  of  the  method  when 
hydrogen  gas  cells  are  used.  This  is  in  direct  contradiction  to  the  con- 
clusion arrived  at  by  Macintosh  eighteen  years  earlier. 

There  is  no  accurate  work,  thus  far,  on  the  application  of  the  method 
to  uni-bivalent  electrolytes. 

Theortical 

The  determination  involves  the  measurement  of  the  potentials  of  a 
concentration  cell  without  diffusion;  a  concentration  cell  with  diffusion 
and  reversible  with  respect  to  the  cation;  and  a  concentration  cell  with 
diffusion  and  reversible  with  respect  to  the  anion. 

The  total  potential  of  the  concentration  cell,  reversible  with  respect 
to  the  cation,  PtH  |  H2SC>4  d  \  H2SO4  c2 1  Ptn»  consists  of  the  algebraic 
sum  of  the  two  electrode  potentials  and  the  potential  at  the  boundary 
of  the  solutions.  On  the  assumption  that  sulfuric  acid  dissociates  into 
two  hydrogen  ions  and  one  sulfate  ion,  the  algebraic  sum  of  the  electrode 
potentials  is  expressed  by  the  well-known  formula 

&-5Tft,s.  a, 

b       cz 

The  potential  at  the  liquid  boundary  is  expressed  by  the  formula 

2Uc-Ua  RT     ci 


8 

The  hydrogen  electrode  in  the  concentrated  solution  is  positive  with  re- 
spect to  the  hydrogen  electrode  in  the  dilute  solution.  At  the  boundary 
of  the  solutions,  the  sulfuric  acid  diffuses  from  the  concentrated  to  the 
dilute  side,  and  since  the  hydrogen  ion  moves  faster  than  the  sulfate 
ion,  the  dilute  side  is  positively  charged  with  respect  to  the  concentrated. 
This  means  that  the  potential  developed  at  the  boundary  opposes  the 
potential  of  the  hydrogen  electrodes.  The  total  potential  of  the  hydrogen 
concentration  cell  is,  therefore,  expressed  by  the  equation 

RT      a       2UC  -  Ua      RT      ci 


[2UC  -  Ua'}  RT      ci  _  3   Ua 
1  '"  2(UC  +  Ua)\    F    H  c*  ~  2  Ua  + 


RT 
Uc    F 


By  the  substitution  of  the  transference  number  of  Nfl,  of  the  anion  for 

Ua/(Ua  +  Uc)   the  equation 

Et^N.Zjln*  (3) 

is  obtained. 

The  total  potential  of  the  concentration  cell,  reversible  with  respect 
to  the  anion  Hg  |  Hg2SO4,  H2SO4Ci  |  H2SO4c2,  Hg2SO4  |  Hg,  consists  of  the 
algebraic  sum  of  the  two  electrode  potentials  and  the  potential  at  the 
boundary  of  the  solutions.  The  algebraic  sum  of  the  electrode  potentials 
is  expressed  by  the  formula 

The  boundary  potential  is  the  same  as  in  the  hydrogen  concentration  cell, 
and  is  in  the  same  direction.  The  algebraic  sum  of  the  sulfate  electrode 
potentials  is  also  in  this  direction.  Therefore  the  total  potential  of  the 
sulfate  concentration  cell  is  expressed  by  the  equation 

_  RT      ci         2UC  -  Ua    RT      ci 

[1         2UC  -  Ua  "1  RT      £1  _        3  Uc        RT  ^    ci 
2  +  2(UC  +  Ua)]    F    H  c,~  2  Uc  +  Ua    F    H  c2' 

By  the  substitution  of  the  transference  number,  Nc,  of  the  cation  for  the 
expression  Uc/(Ua  -+-  Uc)  the  equation  becomes 

E&o4  =  -  Nc  —17  In  - .  (5) 

2,  r          C'2 

The  potential  of  the  concentration  cell  without  diffusion,  PtH  |  0.1  M 
H2SO4,  Hg2SO4,  |  Hg  1  Hg2SO4,  0.01  M  H2SO4  |  PtH,  is  represented  by  the 
equation 

E  =  \Rilnl  (6) 


9 

The  value  E  may  be  obtained  experimentally  from  the  difference  between 
the  potentials  of  the  cells  PtH  1  0.1  M  H2SO4,  Hg2SO4  |  Hg,  and  PtH  1 
0.01  M,  H2S04,  Hg2S04  1  Hg. 

Equation  5  divided  by  Equation  6  gives  ESOJE  =  Nc,  which  expresses 
the  transference  number  of  the  cation  in  terms  of  ES04  and  E.  In  a.  simi- 
lar way  the  expression  EH/E  =  Na,  is  obtained,  as  Na  +  Nc  =  1,  there- 
fore EsoJE-\-Eu/E  =  L;  and 

£so4  +  £H  =  E.  (7) 

It  is  evident  from  Equation  7  that  the  same  value  should  be  obtained 
by  the  sum  of  the  potentials  ESOt  and  EH  as  by  the  difference  of  the  po- 
tentials EQ.QI  and  £0-1. 

Since,  to  obtain  the  total  potential,  Es0t,  the  boundary  potential  is  added 
to  the  electrode  potentials,  while  for  the  total  potential,  Eu,  it  is  subtracted, 
then,  by  a  combination  of  these  as  shown  below,  a  formula  is  obtained 
which  expresses  the  boundary  potential  in  terms  of  ESOi  and  EH- 

RT     ci     (2-3Ng)RTi   Ci   .  RT      Cl       (2-3NJRT     ci 

EH  =  —  In  ---  -  --  —  In  -  ;  ESOt  =  —  -  In  -  H  --  -  --  —  In  -; 

F       cz          2          F       ci  2F       c2  2          F        ci 


RT      ci   ,   2(2-3Na)RT      ci 
2ES04=—  *-  +  —  -  --  -/«- 

2£S04-£H       (2-3Na)RTi   a 


Therefore  the  value  for  the  boundary  potential  may  be  obtained  by  the 
substitution  of  the  measured  potentials  ESOt  and  EH  in  the  above  equation. 

Apparatus  and  Materials. 

The  potential  measurements  were  made  with  an  Otto  Wolff  15,000-ohm 
potentiometer,  using  a  certified  Weston  cell  as  a  standard.  The  solutions 
were  prepared  from  a  commercial  c.  P.  sulfuric  acid  of  1.84  sp.  gr.  and 
were  standardized  by  means  of  sodium  carbonate  prepared  by  the  fusion 
of  c.  P.  sodium  hydrogen  carbonate  in  an  atmosphere  of  carbon  dioxide. 
The  mercurous  sulfate  was  electrolytically  prepared  by  the  Hulett2  method. 
The  hydrogen  was  obtained  by  the  electrolysis  of  5  N  sodium  hydroxide 
solution  using  a  generator  similar  to  that  of  Bodenstein  and  Pohl,3  and 
the  hydrogen  electrodes  were  of  the  ordinary  foil  type.  The  mercury 
used  was  twice  distilled.  All  measurements  were  made  with  the  cells 
contained  in  an  electrically  heated  and  regulated  oil  thermostat  main- 
tained at  a  constant  temperature  of  25°. 

The  concentration  cell  method,  as  previously  shown,  requires  the  con- 
secutive measurement  of  4  distinct  potentials  which  must  be  extremely 
constant  and  reproducible.  Much  experimental  work  was  required  before 
the  satisfactory  system  of  cells  shown  in  Fig.  1  was  developed.  In  this 

2  Hulett,  Phys.  Rev.,  32,  257  (1911). 

3  Bodenstein  and  Pohl,  Z.  Elektrochem.,  11,  373  (1905). 


10 

arrangement  the  connections,  between  the  separate  cells,  are  made  by 
means  of  siphons  (M,  N,  H  and  G).  A  method  whereby  they  could  be 
filled  with  the  proper  solutions  before  being  connected  with  the  arms  of 
the  containers  was  considered  essential.  In  this  way  new  boundaries 
could  be  introduced  without  disturbing  the  electrodes.  Connections 
were  made  with  the  cells  through  the  reservoirs  (RBI  Rb,  Rc,  Rd,  Fig.  1) 
on  the  arms  of  the  containers. 

Arrangement  of  Cells  and  Method  of  Procedure. 

In  Fig.  1,  A  and  B  are  the  mercurous  sulfate  electrodes;  C  and  D  are 
the  hydrogen  electrodes.  A  and  C  contain  O.I  M  and  B  and  D  0.01  M 
sulfuric  acid.  The  electrodes  A  and  C  are  connected  by  the  siphon  H, 
B  and  D  by  the  siphon  G.  The  two  sulfate  electrodes  are  connected  by 
the  siphon  M;  the  two  hydrogen  electrodes  by  the  siphon  N. 

The  containers  were  fastened  in  their  proper  position  and  filled  with  the 
electrode  materials.  The  siphons  H  and  G  were  put  in  place  and  filled  by 
suction.  The  stopcocks  J  and  O,  P  and  K  were  then  closed.  The  hydro- 
gen was  admitted  to  C  and  D  through  the  inlets  S  and  S'  and  bubbled 
through  the  solutions.  It  escaped  through  the  outlets  W  and  W'  into 

M  H  6  V 


R    a^aegfe- 


Fig.  1. — Arrangement  of  cells  as  used. 

chambers  (not  shown)  of  about  10  cc.  capacity.  When  the  hydrogen 
electrodes  became  constant,  the  stopcock  O  was  opened  long  enough  to 
measure  the  potential  E  0  •  i  between  the  sulfate  and  hydrogen  electrodes 
in  0. 1  M  sulfuric  acid  solution.  In  a  similar  way  the  measurement  E  O.QI 


11 

was  made  for  the  sulfate  and  hydrogen  electrodes  in  0.01  M  sulfuric  acid. 
By  the  proper  manipulation  of  the  stopcocks,  the  solutions  in  those  halves 
of  siphons  H  and  G  connected  to  the  sulfate  electrodes  were  emptied. 
The  arms  of  the  siphons  M  and  N  with  the  rubber  stoppers  attached  were 
immersed  in  2  beakers  which  contained  0.1  M  and  0.01  M  sulfuric  acid. 
The  solutions  were  drawn  into  the  arms  of  the  siphons  and  formed  the 
boundary  within  the  stopcocks  t  and  q.  These  siphons  were  then  placed 
in  their  proper  positions  connecting  the  cells.4  The  stopcock  q  was  opened 
and  the  potential  EH  of  the  hydrogen  concentration  cell  measured.  In 
a  similar  way  the  potential  of  the  sulfate  concentration  cell  (.EsoJ  was 
measured. 

The  leads  from  the  electrodes  were  permanently  connected  to  a  switch- 
board so  the  potentials  between  any  two  electrodes  could  be  measured 
by  the  manipulation  of  a  switch  connected  to  the  potentiometer. 

In  the  first  part  of  the  work  the  measurements  showed  considerable 
fluctuation,  which  was  traced  to  the  leakage  of  current  from  the  high 
potential  electrical  circuits  in  connection  with  the  thermostat.  The 
difficulty  was  overcome  by  the  replacement  of  the  water  by  kerosene. 

During  the  development  of  this  work  some  information  was  obtained 
which  may  be  of  assistance  to  others  concerned  with  similar  investigations. 
It  was  found  that  the  length  of  time  required  for  the  mercurous  sulfate 
electrodes  to  reach  a  condition  of  equilibrium  could  be  greatly  reduced 
by  vigorously  shaking  the  sulfuric  acid  and  mercurous  sulfate  in  a  me- 
chanical shaker  before  using  in  the  cells.  The  first  cells  constructed  con- 
tained the  hydrogen  electrodes  in  the  same  chamber  as  the  mercurous 
sulfate  electrode  and  the  potentials  were  found  to  vary  greatly.  This 
was  believed  to  be  due  to  the  catalytic  effect  of  the  platinum  black  which 
was  loosened  by  the  action  of  the  hydrogen  on  the  electrode  and  fell  on 
to  the  mercurous  sulfate.  The  difficulty  was  eliminated  by  the  use  of 
separate  chambers  for  the  electrodes. 

Experimental  Results  with  Sulfuric  Acid. 

The  final  measurements  were  made  and  are  given  in  four  tables  of  which 
I  and  II  are  examples. 

In  these  tables  Col.  EH  contains  the  potentials  of  the  hydrogen  con- 
centration cell  with  diffusion,  PtH  |  0.1  M  H2SO4  |  0.01  M  H2SO4 1  PtH; 
Col.  ES04  those  of  the  sulfate  concentration  cell  with  diffusion,  Hg  Hg2SO4 
0.01  M  H2SO4  |  0.1  M  H2SO4,  Hg2SO4  |  Hg;  Col.  E0.i  the  potentials  of 
the  cell  PtH  |  0.1  M  H2SO4,  Hg2SO4  |  Hg;  and  Col.  EQ.OI  the  potentials 
of  the  cell,  PtH  I  0.01  M  H2SO4,  Hg2SO4  |  Hg.  The  column  headed  "E 
by  EH  +  £304"  contains  the  sums  of  the  values  recorded  in  Cols.  EH 
4  In  the  measurement  for  the  transference  numbers  of  HaSC^  the  reservoirs  (Ra,  Rb> 
RC,  Rd»)  were  filled  above  the  openings  of  the  side  arms.  In  the  later  work  when 
gelatin  was  used  they  were  filled  as  shown  in  the  diagram. 


12 

TABLE  I. 

£  by  £  by 

No.    Date.      Time.  Bar.          EH.  ESO4.  EQ^.         EOQ1.     EH+ESOt.EQ  01  -  EQ  j. 

Mm. 

1  10/13     3:00  P.M.  741.6 0.742020.80260 

2  10/13     4:00  741.6   0.74200  0.80260   

3  10/13     7:30  740.4  0.01137  0.04933  0.74205  0.80275  0.06070  0.06070 

4  10/13     9:00  740.0  0.01139  0.04930  0.74210  0.80274  0.06069  0.06064 

5  10/13  10:30  740.0  0.01139  0.04929  0.74212  0.80276  0.06068  0.06064 

6  10/13  11:30  739.5  0.01141  0.04928  0.74212  0.80279  0.06069  0.06067 

7  10/14  10:00  A.M.  736.0  0.01136  0.04900  0.74203  0.80249  0.06036  0.06036 

8  10/14     1:30  P.M.  734.5  0.01133  0.04913  0.74201  0.80246  0.06046  0.06035 

9  10/14     3:30  734.5  0.01130  0.04918  0.74203  0.80245  0.06048  0.06042 

Av.  0.01136  0.04922  0.74207  0.80263  0  06058  0.06056 

The  cell  was  set  up  at  9:00  A.M.  on  October  13,  1919. 

TABLE  II. 

1  10/15  10: 00  A.M.  739.3  0.741660.80192  

2  10/15  1:30  P.M 0.74209  0.80263  

3  10/15  5:45     0.742000.80268 

4  10/15  7:15     0.742050.80269  

5  10/15  10:00  737.3  0.01136  0.04922  0.74195  0.80256  0.06058  0.06061 

6  10/15  12:00  737.0  0.01127  0.04921  0.74212  0.80257  0.06048  0.06045 

7  10/16  9: 00  A.M.  736.30.011200.049270.742090.802530.060470.06044 

8  10/16  10:30  736.5  0.01121  0.04923  0.74210  0.80247  0.06044  0.06037 

Av.  0.01126  0.04923  0.74206  0.80253  0.06049  0.06047 

The  cell  was  set  up  at  11  P.M.  on  October  14,  1919. 

and  ESOi.  The  column  "E  by  EO.OI  —  HO.I"  contains*  the  differences 
between  the  values  recorded  in  E0.oi  and  E0  }. 

The  0.1  M  and  0.01  M  cells  were  prepared  and  placed  in  the  thermostat 
where  they  remained  for  about  12  hours  to  come  to  equilibrium  before 
the  boundaries  were  introduced.  This  accounts  for  the  blank  spaces  in 
the  tables. 

As  pointed  out  in  the  theoretical  discussion  the  values  recorded  in  column 
EH  +  ESOi  should  be  equal  to  those  recorded  in  column  E0.oi  —  ^o.i- 
The  close  agreement  of  these  values  indicates  the  accuracy  of  the  potential 
measurements.  The  differences  between  the  successive  values  in  each 
column  indicates  the  degree  of  constancy  of  the  cells.  The  differences 
in  columns  E0.oi  and  £0.1  may  be  attributed,  in  part,  to  changes  in 
barometric  pressure,  for  which  corrections  have  not  been  applied,  as  such 
corrections  are  unnecessary  for  the  calculations  in  which  the  measurements 
are  used. 

The  remarkable  agreement  between  the  averages  in  the  different  tables 
indicates  the  reproducibility  of  the  work. 

In  the  theoretical  treatment  formulas  were  given  by  means  of  which 
the  values  of  E,  EH,  ESO«  and  EB  can  be  calculated.  Table  III  contains 
a  summary  of  such  calculated  values  together  with  the  measured  values. 


13 


TABLE  III.  —  COMPARISON  BETWEEN  CALCULATED  AND  MEASURED  POTENTIALS. 

E'.  Ef.  E.  EB.  Esot.  £B. 

Calc.  from    /  Cond.    0.10511     0.06693     0.08883     0.014716     0.06407    0.03781 
\Fz.Pt.0.08072     .......     0.06054    0.011301     0.04918    0.02908 

Measured  ..............     0.06054     0.011310     0.04925     0.02906 


These  calculations  involve  the  ratio  otid/otjCs.  It  has  been  customary 
to  use  conductivity  values  in  its  calculation.  Since  the  work  of  Jones 
is  probably  the  most  reliable  on  the  conductivity  of  sulfuric  acid,  his  re- 
sults were  used  in  these  calculations.  This  ratio  may  also  be  obtained 
from  freezing-point  data.  The  values  obtained  from  these  two  sources 
are  decidedly  at  variance.  No  freezing-point  data  are  available  for  the 
degree  of  dissociation  of  0.1  M  sulfuric  acid.  However,  a  complete 
table  is  given  by  Lewis  and  Linhart5  for  concentrations  between  10  ~2 
and  10~6  molar.  The  degree  of  dissociation  given  by  Lewis  and  Linhart 
for  0.01  M  sulfuric  acid  was  substituted  in  the  equation  for  E  together 
with  the  measured  potential  (0.06054),  and  the  equation  solved  for  the 
degree  of  dissociation  for  0.1  M  sulfuric  acid.  In  the  curve  of  Fig.  2 
the  abscissas  are  the  molar  concentrations  and  the  ordinates  the  degrees 

of  dissociation.  The  portion  indicated 
by  the  solid  line  was  obtained  from  the 
freezing-point  data  and  the  broken 
portion  is  an  extension  to  include  the 
value  calculated  from  the  potential 
measurements.  Since  this  is  a  smooth 
curve,  the  indication  is  that  the  point 
obtained  from  the  potential  measure- 
ments is  approximately  the  same  as 
would  have  been  obtained  from  the 
freezing-point  determination.  In  every 
instance  the  results  obtained  when  the 
freezing-point  values  are  used  in  the 
ratio  aiCi/azCz  show  better  agreement 
with  the  measured  potentials  than  when 
the  conductivity  values  are  used.  The 
latter  results  are  in  all  cases  higher  than 
the  measured.  It  should  be  noticed, 

however,  that  the  exact  agreement  between  the  measured  and  calculated 
values  for  E  is  to  be  expected,  since  it  was  from  this  measured  value  of  E 
that  G  was  calculated.  The  close  agreement  between  the  measured  and 
calculated  values  of  EH,  £SO4  and  EB  is  a  true  indication  of  the  correctness 
of  the  value  0.2973  for  the  degree  of  dissociation  of  0.1  M  sulfuric 
acid. 

5  Lewis  and  Linhart,  J.  Am.  Chem.  Soc.,  41,  1959  (1919). 


/oo 


90 


80 


•70 


60 


50 


40 


30, 


MOLAR  CONCENTKATION 


D./  0.O/        O.OOt     O.OOOI  O.OOOOI  O.OOOOOI 

Fig.  2. — Dissociation-concentration 
curve. 


14 

It  is  important  to  note  that  all  of  the  values  thus  far  calculated  are  based 
on  the  assumption  that  sulfuric  acid  dissociates  entirely  into  two  hydrogen 
ions  and  one  sulfate  ion.  Column  Ef  shows  the  values  for  E  calculated 
on  the  assumption  that  the  sulfuric  acid  dissociates  into  one  hydrogen 
ion  and  one  hydrogen  sulfate  ion.  The  fact  that  the  measured  potentials 
agree  so  well  with  those  calculated  on  the  first  assumption  and  do  not  agree 
with  those  calculated  on  the  second  assumption  is  a  strong  indication  that  the 
sulfuric  acid  dissociates  almost  entirely  into  3  ions  at  these  concentrations. 

It  has  been  noticed  by  others  that  the  calculated  values  for  potential 
measurements  are  always  higher  than  the  measured  values  when  conduc- 
tivity dissociation  ratios  are  used.  Ferguson6  in  his  work  on  hydrochloric 
acid  attributed  the  difference  to  the  fact  that  the  formula  assumes  the 
complete  dissociation  of  the  acid.  As  the  acid  is  not  completely  dissociated 
the  formula  does  not  exactly  represent  the  facts  and  must  be  corrected 
so  as  to  include  the  undissociated  acid.  Such  a  correction  was  made  for 
hydrochloric  acid  and,  when  applied  to  the  formulas  involving  conductivity 
ratios,  gave  values  which  agreed  more  closely  with  those  measured.  A 
similar  correction  can  be  developed  for  the  sulfuric  acid  concentration  cell. 

When  two  faradays  of  electricity  pass  through  a  sulfuric  acid  concentra- 
tion double  cell,  one  mol  of  acid  is  transferred  from  one  concentration  to  the 
other.  The  electrical  work  which  accompanies  this  change  is  represented 
by  W  =  2  EF.  The  osmotic  work  required  to  effect  this  same  change 
is  usually  represented  by  W  -  3  RT  In  Ci/cz.  This  assumes  that  the  acid 
is  completely  dissociated  into  3  ions.  Since  it  is  not  completely  dissociated 
what  actually  happens  is  (1)  the  transference  of  an  amount  of  hydrogen 
ion  equal  to  twice  the  concentration  times  the  dissociation  of  the  acid; 
(2)  the  transference  of  an  amount  of  sulfate  ion  equal  to  the  concentration 
times  the  dissociation  of  the  acid;  (3)  the  transference  of  an  amount  of  un- 
dissociated acid  equal  to  the  concentration  of  the  undissociated  acid.  The 
general  expression  which  represents  the  sum  of  the  osmotic  work  in  (1) 

and  (2)  is  Wi  =  aZRT  lnc± 

Cz 

Similarly  the  osmotic  work  in  (3)  is  W  =  (I  —  a)RT  In  -.     In  the  appli- 

Cz 

cation  to  sulfuric  acid  (d)  in  (Wi)  becomes  2ciH+  =  2  CIOL'  =   CiSO4~~; 
and  Cz  becomes  2c2H+  =  2cz  a"  =  c2SO4     . 

Similarly  Ci  in  Wz  becomes  CiH2SO4  =  Ci  (1—  a');  and  cz  becomes  c2H2- 
SO4  =  c2(l  —  a*)\  and,  as  the  total  electrical  work  is  equal  to  the  total 
osmotic  work, 

W  =  2EF  =  <x3RTln—ff  +  (l-« 
Cict 


E  =  - 

2  F 

6  J.  Phys.  Chem.,  20,  326  (1916). 


15 

This  formula  cannot  be  taken  as  absolutely  correct  since  it  assumes  that 
the  dissociation  is  the  same  in  both  concentrations,  which  is  not  true. 

The  most  reliable  value  that  can  be  used  for  a  is  '  in  which  a' 

A 

is  the  degree  of  dissociation  in  c\  and  a"  is  the  degree  of  dissociation  in  c*. 

Col.  E"  Table  III  shows  the  result  of  the  application  of  this  correction. 
It  is  evident  that  the  correction  is  an  improvement  since  the  difference 
(0.00639)  between  the  measured  value  and  that  calculated  from  the  cor- 
rected formula  is  much  less  than  the  difference  (0.01829)  between  the 
measured  value  and  that  calculated  from  the  usual  formula. 

In  the  theoretical  part  of  this  work  is  was  shown  that  the  boundary 


o  _    o     AT       J2T*  r 

potential  can  be  calculated  from  the  formula  EB  =  -  -  —  In  —  ; 

2          F        c2 

9  £T  77" 

also  that  EB  =  —  —  —     —  .     Column  EB  contains  the  results  from  the 
3 

calculation  by  the  first  formula.  Again  the  close  agreement  between 
the  measured  and  calculate  values  in  the  case  of  the  freezing-point 
ratio  and  lack  of  agreement  in  the  case  of  the  conductivity  ratio  are 
evident. 

Maclnnes7  has  developed  a  formula  for  boundary  potentials  of  uni- 
univalent  electrolytes  which  involves  the  transference  number  of  the  cation 
and  the  potentials  of  the  cells  with  and  without  diffusion.  He  states 
that  it  "contains  no  assumption  regarding  the  concentration  of  the  ions 
of  the  solutions."  In  the  following  development  the  same  reasoning  is 
applied  to  the  uni-bivalent  acid,  sulfuric  acid,  on  the  assumption  that  it 
dissociates  into  two  hydrogen  ions  and  one  sulfate  ion. 

When  two  faradays  of  electricity  pass  through  the  cell  the  net  result 
is  the  transference  of  one  mol  of  sulfuric  acid  from  the  concentrated  to  the 
dilute  side.  The  current  is  carried  across  the  boundary  between  the  two 
solutions  by  the  transference  of  2  Nc  gram  ions  of  hydrogen  ions  in  one 
direction  and  1  —  Nc  gram  ions  of  sulfate  ions  in  the  opposite.  The  osmotic 
work  at  the  boundary  is  proportional  to  the  algebraic  sum  of  the  number 
of  gram  ions  that  have  passed  through  it.  Therefore  the  osmotic  work 
W  is  proportional  to  3NC  —  1.  The  electrical  work  which  accompanies 
the  transference  of  one  mol  of  sulfuric  acid  from  the  concentrated  to  the 
dilute  side  is  equal  to  the  product  of  the  electromotive  force  of  the  cell 
and  the  number  of  faradays  required  to  effect  the  transference.  Since 
this  is  so,  the  following  relation  holds. 

2EF:2EsF::3:3Nc  -  1 

a.ndEB  =  E(3NC  -  l)/3;  forE,  -^p  may  be  substituted  since  it  has  been 
7  Maclnnes,  /.  Am.  Chem.  Soc.,  37,  2301  (1915). 


16 


shown  that  N    =  — §^4.    The  formula  then  becomes 
iSt 

EB  =  £so<  (3NC  -  1)  /3NC. 

Substituting  the  correct  values  for  Nc  and  ES04  as  measured,  the  value 
0.02904  is  obtained.  This  is  in  almost  perfect  agreement  with  the  meas- 
ured value  0.02906  and  proves  the  validity  of  the  formula. 

That  this  expression  EB  =  ESOt  (3NC  —  1)  /3Ne  is  but  another  form  of 


c\ QAT      7?  "7""          r 

the  usual  expression  EB  =  — - — -  — -  In  -  for  boundary  potential,  can 

2          r         €2 

readily  be  shown,  since 

EB  =  jj^4  (3Ne  -  1)  (9) 

and 


Substituting  in  (9) 

Nc In  -  RT      r. 

EB  =        2    F       c2  (3Nf  _  !)  =  ££.  tn  *  (3Nc  _  1} 

3N<  F 

is  obtained;  as  (3NC  -  1)  =  (2  -  3Na) 

RT      a  2  -  3Na  RT  ,    Cl 

EB  —  —  In-   (3NC  —  1)  =  —  In-. 

F        c2  2          F        c2 

Therefore 

2  -  3Na  RT  7    Cl       2E80i  -  E 


t  /OA7        , 
EB  =  _  (3Nc  _  D  = 


3Ne   N  2  F        c2  3 

A  consideration  of  these  formulas  indicates  the  advantage  of  the  formula 
(2  £S04— -EH)/3  since  it  contains  no  assumption  regarding  the  concentration 
of  the  ions,  nor  does  it  require  a  knowledge  of  the  transference  numbers. 
The  averages  of  EH,  ESOt,  and  E  from  a  few  of  the  tables  obtained  are 
contained  in  Table  IV,  together  with  the  transference  numbers  calculated 
from  them. 

TABLE  IV. 

SUMMARY   OP   POTENTIALS   AND   TRANSFERENCE   NUMBERS. 
T  KI  j?  j?  Eor  N"-  Na- 

Table.  /£„.  -rWu- 


II 

0.01136 

0.04922 

0.06056 

0.1875 

0.1875 

III 

0.01126 

0.04923 

0.06047 

0.1862 

0.1862 

IV 

0.01137 

0.04929 

0.06059 

0.1875 

0.1874 

V 

0.01126 

0.04927 

0.06053 

0.1868 

0.1868 

Av. 

0.01131 

0.04925 

0.06054 

0.1868 

0.1868 

To  facilitate  the  comparison  of  the  value  obtained  in  this  investiga- 
tion with  those  obtained  on  others,  a  summary  of  such  values  is  contained 
in  Table  V. 


17 

Attention  should  be  called  to  the  fact  that  the  values  recorded  in  columns 
En/E  and  1—ESOJE  of  Table  IV  are  determined  from  separate  and  dis- 
tinct potential  measurements.  The  agreement  between  the  successive 
values  in  each  column  and  between  the  averages  of  the  two  columns  demon- 
strates the  reliability  of  the  concentration  cell  method  for  the  determination 
of  the  transference  numbers  of  sulfuric  acid. 

TABUS  V. 
SUMMARY  OP  TRANSFERENCE  NUMBERS  OF  SULFURIC  ACID. 

Investigator^  Concentration.  Te0^p-  N*'  **£%£*** 

Bein  1898  0.24%  11  0. 175=^=3  0.1804 

Mclntosh  1898  1.0-0. 001 M  18  0.174=*=  18  0.1817 

Starck  1899  0.5-0.6%  17-20  0.145=*=?  

Jahn  and  Huybrechts  1902  0.06-0. 005  M  18  0.176=»=4  0.1837 

Eisenstein  1902  Q.124M  18  0.168  ±3  0.1757 

Eisenstein  1902  0.01M  30  0.188=*=!  0.1825 

Tower  1904  0.1  M  20  "0.1805  0.1860 

Tower  1904  0.01  If  20  0.1809  0.1864 

Whetham  and  Paine  1908  0.05M  18  0.184  0.1917 

France  1920  0.1-O.OlJlf  25  0.1868  0.1868 

Experimental  Results  with  Sulfuric  Acid  Containing  Gelatin. 

The  properties  of  hydrophile  colloids  have  been  the  subject  of  many 
investigations  during  the  past  few  years.  So  far,  no  entirely  satisfactory 
explanation  has  been  offered  for  their  action  in  the  presence  of  electrolytes. 
The  theories  advanced  are  based  largely  on  the  measurements  of  osmotic 
pressure,  conductivity,  swelling  and  transference  numbers. 

There  appear  to  be  but  three  articles  in  the  literature  dealing  with  the 
influence  of  colloids  on  transference  numbers  and  in  each  instance  the 
analytical  method  was  used. 

Paul  Richter9  investigated  the  influence  of  gelatin,  gum  arabic,  agar- 
agar,  and  peptone  on  the  transference  number  of  the  chloride  ion  of  lithium, 
potassium  and  hydrogen  chlorides. 

A.  Mutscheller10  investigated  the  influence  of  gelatin  on  the  transfer 
ence  numbers  of  silver  nitrate,  cupric  sulfate  and  zinc  sulfate  solution 
which  contained  definite  quantities  of  a  1%  gelatin  solution. 

According  to  his  results  the  transference  numbers  of  the  nitrate  and 

8  The  values  and  the  limits  of  accuracy  of  the  first  six  investigations  are  taken 
from  MacBain's  abstract  of  transference  data  (/.  Wash.  Acad.  Sci.,  9,  11  (1905)).     In 
the  first  six  investigations  the  analytical  method  was  employed.     According  to  Mac- 
Bain  the  results  of  Jahn  and  Huybrechts  and  of  Tower  are  probably  the  most  reliable. 
Whetham  and  Paine  employed  the  conductivity  method.     The  values  in  the  last  column 
were  obtained  from  the  values  in  the  preceding  column  by  the  application  of  the  tem- 
perature coefficients  given  by  Tower  (/.  Am.  Chem.  Soc.,  26,  1038  (1904). 

9  Richter,  Z.  physik.  Chem.,  80,  449  (1912). 

10  Mutscheller,  Met.  Chem.  Eng.,  13,353  (1915);  J.  Am.  Chem.  Soc.,  42,  442  (1920). 


18 

sulfate  ions  decrease  with  an  increase  in  the  quantity  of  gelatin  solution 
added.  By  the  addition  of  sufficient  quantities  of  gelatin  solution,  even 
negative  values  were  obtained.  He  states  that  when  the  transference 
number  of  the  anion  is  zero  the  conditions  are  most  favorable  for  the 
deposition  of  the  metal.  The  effect  of  the  gelatin  is  accounted  for  on  the 
assumption  that  it  is  positively  charged  and  forms  an  "absorption  com- 
pound" with  the  anions.  This  results  in  the  partial  or  complete  neu- 
tralization or  even  reversal  of  the  original  charge  on  the  ions.  The  re- 
sults obtained  by  Mutscheller  for  the  sulfate  and  nitrate  ions  show  effects 
of  gelatin  far  in  excess  of  those  observed  by  Richter  for  the  chloride  ion. 

It  is  well  to  emphasize  here  that  the  results  obtained  by  Mutscheller, 
if  correct,  are  indeed  remarkable,  but  it  is  the  opinion  of  the  author  that 
an  error  has  been  made  in  the  calculations  or  in  the  recorded  data.  This 
subject  is  under  investigation  at  the  present  time. 

Mutscheller10  explains  the  effect  of  gelatin  on  the  transference  numbers 
of  silver  nitrate,  cupric  sulfate  and  zinc  sulfate  by  the  assumption  that 
gelatin  is  positively  charged  and  "absorbs"  the  negative  ions.  This 
causes  a  decrease  in  their  velocity.  According  to  Nernst  the  potential 
at  the  boundary  of  two  solutions  of  different  concentration  depends  upon 
the  difference  in  velocities  of  the  ions.  If  the  theory  of  Mutscheller  is 
true  the  presence  of  gelatin  in  such  solutions  should  change  the  boundary 
potential.  Then  measurements  of  the  transference  numbers  of  sulfuric 
acid  by  this  method  would  determine  whether  gelatin  affected  the  boundary 
potential. 

Since  gelatin  precipitates  the  heavy  metals,  it  was  obvious  that  precipi- 
tation would  result  if  it  were  added  to  a  sulfuric  acid  solution  saturated  with 
mercurous  sulfate.  Since,  however,  the  influence  of  the  gelatin  on  trans- 
ference numbers  is  due  only  to  its  effect  on  the  boundary  potential,  it  is 
unnecessary  to  introduce  gelatin  into  the  electrode  containers. 

The  cells  were  prepared  as  described  and  the  siphons  connect'ng  the 
hydrogen  and  sulfate  electrodes  were  filled  with  0.1  M  and  0.01  M  sol- 
utions of  sulfuric  acid  which  contained  a  definite  concentration  of  gelatin. 
They  were  then  placed  in  the  reservoirs,  with  the  ends  immersed  in  solu- 
tions of  the  same  concentrations  as  that  which  surrounded  the  electrodes. 
The  measurements  were  made  as  before,  but  showed  a  gradual  progres- 
sive change.  It  was  discovered  that  this  was  due  to  the  diffusion  of 
the  gelatin  from  the  siphons  into  the  reservoirs  and  then  into  the  solu- 
tion which  surrounded  the  electrodes.  This  made  it  necessary  to  devise 
a  method  which  would  prevent  the  diffusion  and  at  the  same  time  intro- 
duce no  new  potentials.  Several  devices  were  tried  in  which  use  was 
made  of  glass  wool,  filter  paper,  glass  capillaries,  and  cotton  wicks, 
before  the  following  satisfactory  method  was  found. 

Ordinary  cotton  lamp-wicks  were  carefully  washed  by  boiling  in  acid 


19 


of  the  same  concentration  as  used  in  the  cells.  After  washing  and  dry- 
ing they  were  kept  in  0.1  M  and  0.01  M  sulfuric  acid  solutions.  Cells 
were  prepared  and  so  filled  that  the  solution  rose  in  the  inner  tube  to  the 
level  L  indicated  in  Fig.  III.  Gelatin  solution  identical 
with  that  in  the  siphon  S  was  filled  in  the  reservoirs  to 
the  level  L.  A  wick  W  previously  saturated  with  acid 
solution  containing  no  gelatin  was  hung  over  the  side  of 
the  inner  tube  so  that  one  end  of  it  was  immersed  in  the 
plain  solution  of  the  inner  tube  and  the  other  in  the  gela- 
tin solution  in  the  reservoir.  This  arrangement  effectively 
eliminated  the  diffusion,  provided  the  solutions  in  the 
inner  tube  and  in  the  reservoir  were  maintained  at  the 
same  level.  No  new  potentials  were  introduced  by  this 
arrangement.  All  of  the  measurements  were  made  with 
cells  prepared  in  this  manner.  Measurements  were 
made  with  concentrations  of  gelatin  over  a  range  of 
0.5  to  20.0%.  The  results  of  these  measurements 
are  contained  in  18  tables  of  which  Table  I  is  a 
sample. 


Fig.  Ill— Detail 
of  reservoir. 


Expt.    Date.    Time. 


1  1/14  12: 30  A.M. 

2  1/24     9:30 

3  1/24  11:50 


TABLE  VI. — TYPICAL  EXPERIMENTS. 

Bar.  En-  Eso*-  E0.1-  E0.l. 

Mm.         Using  0.5%  gelatin. 

743.8  0.74189  0.80260 

748.4  0.74205  0.80264 

748.4  .  .  0.74203  0.80260 


Ehn 


Eby 


Using  5%  gelatin  siphons  introduced  at  1  .P.M 


4  1/24  1:00  P.M. 

5  1/24  5:00 

6  1/24  11:00 

7  1/25  10: 30  A.M. 

Av. 


747.8  0.01295  0.04750  0.74199  0.80235 
749.6  0.01290  0.04743  0.04210  0.80220 
751.0  0.01292  0.04740  0.74217  0.80237 
754.2  0.01290  0.04779  0.74213  0.80260 
0.01290  0.04754  0.74213  0.80239 


0.06033  0.06010 

0.06032  0.06020 

0.06069  0.06047 

0.06044  0.06026 


The  cell  was  set  up  on  Jan.  23  at  2: 30  P.M.     The  averages  do  not  include  the  first 
four  sets  of  readings. 

In  these  tables  the  same  arrangement  of  the  data  has  been  followed  as 
in  the  previous  tables.  In  order  that  a  comparison  of  the  values  recorded 
in  the  separate  tables  may  readily  be  made  the  average  values  in  each 
table  together  with  the  transference  numbers  calculated  thereform  have 
been  summarized  in  Table  VII. 

The  headings  of  Cols.  2,  3,  4,  and  5  have  the  same  significance 
as  before.  Cols.  6,  7,  8,  and  9  contain  the  transference  numbers  cal- 
culated from  the  values  in  Cols.  2,  3,  4,  and  5,  as  indicated  in  the  head- 


20 


c  >o 

38 


Tf  C^  CO 

0^  O^  O^ 
OOO 


i  f>-        Ot^O5        t~-  00  00        Is-  CO  >C 

**^        CO  O^  O^        CO  CO  CO        lp~ *  CO  CM 
'O       O  C5  O5       OOO       OOO 


O  I-H  O        I-H  i— i  i-»        i— i  O  O 


!>!>!> 

o  o  o'     o  o  o' 


iC  O  I—  00  "tf  i—  ( 
(Mi-*i-<  (MCOCO 
OCOCO  lO  lO  1C 


o  o  o     o  o  o     o  o  o 


CO  Cl  00 

t^-  I-H  O5  O5C1O5 

COT^CO  COCOCO 

o  o  o  o  o'  o 


CO  lO  O^  O5  <N  i—  ( 

t^OO  CO"t"* 

COCOCO  COCOCO 

o'oo  ooo 


t>  o  ca      oo  Oi  Oi      ic  ic  ic      cococo 

CO  T+I  CO        CO  CO  CO        CO  CO  CO        CO  CO  CO 

o  o  o  ooo  ooo  ooo  ooo  odd  odd  ooo  ooo 


O        »O  i-HCO 
<N        (M  O  T-I 

co      co  co  co 


CO  CJ5 
O 
CO  CO 

o'  o     ooo 


CO  CO  CO  «OOOl>        1C 

I-IT-H^  "^TfriTti 

i-<        W  (M  ci  <N  (N  (N 

d  odd  odd    o 


O  CO        1-1  !>•  Oi        I>  (N  O        CO 
iC»C        (MCO(M        (MOii-H        I-H 


OOo   OOO 


OOO   OOO 


OOO   OOO 


^f  t^*  i—*  O^  1C  CO  C^Q  Oi  CO  O^  *C 

Oi  O  t^COO  OCOCO  CQCOTti 

§COCO        >C»CtC  tCCOcO  COCOCO  COCOCO 

OO        OOO  OOO  OOO  OOO 


ooo  ooo  ooo  ooo  ooo  ooo  ooo  ooo  ooo 


§^o  t^osco  b-oo 

..I-ITI  ??^^  ^?tr 

CO  CO  CO        CO  CO  CO        C^  CQ  C^        C^  C^l  ' 

ooo  ooo  odd  odd  o'o'o".  ddo  ooo  ooo  ooo 


Ob~  T}« 

OOO  O5 


CO  CO 


§8: 


00 


L-O 

1C  ( 


p  p  p  o  pop  p  < 

d  odd  odd  odd  dod  o'oo  odd  ooo  odd  odd 


*•£ 

V 


21 


ings.  Col.  10  contains  the  sum  of  the  Na  and  Nc  values  of  Cols.  7  and  9 
and  should  always  be  equal  to  unity.  The  deviation  from  unity  is  an 
indication  of  the  small  error  of  the  potentials  used  in  their  calculation. 
The  accuracy  with  which  the  potentials  of  EH  and  5S04  can  be  dupli- 
cated in  the  presence  of  gelatin,  is  shown  by  the  closeness  with  which  the 
averages  for  any  two  tables  of  the  same  concentration  agree.  From  a 
comparison  with  similar  values  in  the  previous  tables,  it  is  plainly 
evident  that  when  gelatin  is  present  the  agreement  is  less  satisfac- 
tory than  when  it  is  not.  This  lack  of  agreement  becomes  greater 
the  higher  the  concentration  of  gelatin.  Table  VIII  is  a  summary  of  the 
averages  of  the  potentials  and  transference  numbers  contained  in  Table 
VII. 


TABLE  VIII. — SUMMARY  OF  POTENTIALS  AND  TRANSFERENCE  NUMBERS. 


%  Gel. 
0.0 
0.5 
1.0 
2.0 
2.5 
3.0 
5.0 

10.0 

15.0 

20.0 


*«. 

0.01136 
0.01290 
0.01494 
0.02741 
0.02682 
0.03181 
0.03755 
0.03735 
0.04065 
0.04155 


0.04918 
0.04784 
0.04563 
0.03749 
0.03266 
0.02824 
0.02408 
0.02410 
0.02243 
0.02068 


0.187 
0.213 
0.247 
0.407 
0.442 
0.524 
0.620 
0.613 
0.668 
0.685 


0.02906 
0.02746 
0.02544 
0.01676 
0.01283 
0.00822 
0.00354 
0.00362 
0.00140 
-0.00006 


A  consideration  of  the  values  recorded  for  Na  shows  that  they  increase 
with  increase  in  concentration  of  gelatin.  The  relation  between  the  trans- 
ference number  of  the  anion  and  concentration  of  gelatin  is  shown  by  the 
curve  in  Fig.  4.  In  this  curve  the  transference  numbers  are  plotted  as 


0.700 
0.600 
0.500 
0.400 
0300 

1 

^ 

1 

/ 

§ 

/ 

p 

y 

O./OD 

Ff/i 

?  CfNT. 

6£i.AT 

H£ 

Q  /£>  J2  t4  /6 

Fig.  4. — JVa-gelatin  curve. 


ordinates  and  the  concentrations  of  gelatin  as  abscissas.  The  change 
in  transference  number  with  increase  in  gelatin  is  rapid  at  low  gelatin 
concentrations,  is  gradual  between  3  and  5%,  and  above  this  is  not  appreci- 


22 

able.  If  this  represents  an  actual  increase  in  the  migration  velocity  of 
the  anion,  then  there  must  be  a  corresponding  decrease  in  the  boundary 
potential  (£B)-  The  values  in  the  columns  headed  EB  and  Na  indicate 
such  changes.  ^  Since  the  boundary  potential  is  opposed  to  the  electrode 
potentials  in  the  case  of  the  hydrogen  concentration  cell  (EH)  and  is 
added  to  the  electrode  potentials  in  the  case  of  the  sulfate  concentration 
cell  (ESOi)  a  decrease  in  EB  would  result  in  an  increase  in  the  value  of 
EH  and  a  decrease  in  ESOi.  That  such  changes  do  take  place  is  indicated 
by  the  values  in  the  columns  headed  EH  and  ESOi. 

It  has  been  shown  that  the  boundary  potential  depends  on  the  trans- 
ference numbers  of  the  ions  and  the  ratio  of  their  concentrations  in  the 
two  solutions.  Therefore  a  change  in  E-Q  would  result  from  a  change  in 
concentration  or  a  change  in  transference  number. 

The  value  of  EB  would  be  reduced  by  making  the  concentration  of  the 
solutions  more  nearly  equal.  When  exactly  equal  EB  would  be  zero,  and 
when  the  concentration  of  the  0.1  M  solution  became  less  than  that  of  the 
0.01  M,  the  direction  would  be  reversed. 

To  determine  whether  or  not  concentration  changes  are  produced  by  the 
gelatin,  concentration  cells  of  the  type  PtH  I  0.1  M  H2SO4)KC1  0.1  M 
H2SO4  +  gel.  |  PtH  and  PtH  ]  0.01  M  H2SO4 1  KC1  |  0.01  M  H2SO4  +  gel.  1 
PtH  were  used.  The  data  from  these  measurements  are  summarized 
in  Table  IX. 

TABLE  IX. 

0.1  M.  0.01  M. 

%Gel.  Clf  £x.  C2  Ez. 

0  0.05946  0.012340  

1  0.05694  0.00070  0.007684  0.01216 

2  0.05670  0.00122  0.002172  0.04458 

3  0.05542  0.00181  0.000430  0.08609 

4  0.05356  0.00268  0.000144  0.11418 

It  was  impossible  to  work  with  concentrations  of  gelatin  above  4%  because  of  the 
excessive  foaming  of  the  solutions. 

The  first  column  contains  the  percentage  of  gelatin  in  the  acid  in  one- 
half  the  cell.  The  columns  Ex  and  Ez  contain  the  measured  potentials 
of  the  cells  Ex  and  E2  when  0.1  M  and  0.01  M  solutions  are  used.  In 
columns  C\  and  Cz  are  the  hydrogen-ion  concentrations  in  0.1  M  and 
0.01  M  solutions  with  gelatin,  calculated  by  the  use  of  the  formula  for  con- 
centration cells  in  which  boundary  potential  has  been  eliminated.  The 
results  in  columns  C\  and  C2  show  that  gelatin  produces  a  relatively  small 
decrease  in  the  hydrogen-ion  concentration  of  the  0.1  M  solution,  and  a 
much  greater  relative  decrease  in  the  0.01  M  solution.  The  hydrogen-ion 
concentration  of  the  0.1  M  solution  is  always  greater  than  that  of  the 
0.01  M;  therefore  the  reversal  of  the  boundary  potential  (EB)  as  shown 
in  Table  VIII  cannot  result  from  the  concentration  changes  produced  by  the 


23 

gelatin.  Since  EB  can  be  decreased  or  reversed  only  by  a  change  in  con- 
centration or  transference  number,  the  observed  change  must  be  due  to 
a  change  in  the  transference  number. 

Since  it  has  been  shown  above  that  the  gelatin  produces  changes  in  the 
hydrogen-ion  concentration,  new  potentials  are  developed  at  the  boundaries 
between  the  solutions  in  the  wicks  and  the  gelatin  solution  in  the  reser- 
voirs. The  locations  and  directions  of  the  boundary  potentials,  EB, 
Ex  and  Ez  together  with  .EH  and  ESO*  are  represented  digrammatically 
in  Fig.  5.  The  location  of  the  boundary  potentials  is  shown  also  by  the 
same  letters  in  Fig.  1.  EB  represents  the  potential  within  the  siphon,  that 
is,  the  potential  which  has  been  considered  thus  far.  Ex  and  Ez  repre- 
sents the  potentials  at  the  contact  of  the  solutions  in  the  reservoirs. 
EH  and  E$Q4  are  the  measured  potentials  and  are  the  algebraic  sums  of 
the  potentials  at  the  electrodes  and  the  boundary  potentials  Ex,  EB, 
and  Ez. 

The  potentials  Ex,  EB,  and  Ez  which  result  from  the  presence  of  the 
gelatin  can  be  calculated  from  the  data  in  Table  IX  by  the  use  of  the  usual 
formula  for  boundary  potential.  These  calculations  were  made  and  the 
results  are  included  in  Table  X.  The  potentials  at  Ex  and  Ez  are  oppo- 
sitely directed  and  the  resultant  potential  is  therefore  their  difference. 
These  differences  are  recorded  in  the  column  headed  EZ  —  EX.  The  total 
potential  at  EB  is  opposed  to  the  resultant  potentials  EZ  —  EX  and  may  be 
considered  as  the  sum  of  the  original  boundary  potential  EB  (0.02906) 

and    the    potential    resulting   from  £« 

the  changes  in  concentration  pro- 
duced by  the  gelatin.  Therefore  the 
differences  between  the  total  poten- 
tials  E'B  and  the  original  potential 
EB  (0.02906)  is  that  due  to  the 
changes  in  concentration  produced 
by  the  gelatin.  The  values  of 
these  differences  are  recorded  in 
the  column  headed  E'B -0.02906. 
As  the  values  in  the  column  headed 
E'B- 0.02906  are  practically  iden- 
tical  with  those  in  EZ—EX  and  op- 
positely directed,  their  combined  Fig.  5.-Diagram  of  potentials, 
effect  must  be  zero.  This  shows  that  the  potentials  Ex  and  Ez  at  the 
contacts  between  the  solutions  in  the  wicks  and  the  gelatin  solutions  in  the 
reservoirs  are  entirely  compensated  by  the  potential  (E'B  —  0.02906) 
simultaneously  developed  at  the  boundary  EB.  Therefore  any  boundary 
potential  produced  by  the  introduction  of  gelatin  cannot  result  from 
changes  in  concentration.  The  experimental  data,  however,  show  that 


24 

the  boundary  potential  EB  is  changed  by  the  addition  of  gelatin.  Since 
this  cannot  be  due  to  concentration  changes  it  must  result  from  a  change 
in  the  transference  numbers  of  the  hydrogen  and  sulfate  ions  or  from  an 
actual  change  in  the  kind  of  ions  present.  This  may  be  effected  in  sev- 
eral ways;  (1)  by  the  removal  of  either  ion  as  the  result  of  its  being 
selectively  adsorbed  by  the  gelatin ;  (2)  by  a  change  in  the  velocity  of 
either  ion ;  (3)  by  chemical  reaction  with  the  gelatin  resulting  in  the  forma- 
tion of  new  ions. 

TABLE  X. — BOUNDARY  POTENTIAL  CALCULATIONS. 

%Gel.        EH.  Es04.  EB.  E*.  Ez  Ez-  Ex          EB     -0.02906.E'B 

1  0.01494    0.04563     0.02544     0.00077     0.00878    0.00801     0.00804     0.0371 

2  0.02941     0.03749     0.01676     0.00085     0.03215    0.03107     0.03124     0.0603 

3  0.03181     0.02824     0.00822     0.00132    0.06210     0.06078    0.06094     0.0900 

4      0.00196     0.0825      0.08054     0.08054    0.1095 

Since  the  conductivity  of  a  solution  is  affected  by  any  change  in  the 
number  and  the  mobility  of  its  ions,  it  was  thought  that  conductivity 
measurements  would  furnish  information  as  to  the  nature  of  the  influence 
of  the  gelatin.  Measurements  were  made  of  the  conductivity  of  0 . 1  M 
and  0. 01  M  sulfuric  acid  solutions  which  contained  different  concentrations 
of  gelatin.  The  concentration  of  gelatin  was  varied  from  0  to  20%.  As 
it  was  necessary  to  apply  a  correction  for  the  conductivity  of  the  gelatin 
in  conductivity  water,  a  series  of  measurements  was  made  with  gelatin 
solutions  over  this  same  range  of  concentration.  The  corrected  conduc- 
tivity values  are  recorded  in  Table  XI. 

TABLE  XI. — CONDUCTIVITY  OF  SULFURIC  ACID  SOLUTIONS  IN  PRESENCE  OF  GELATIN 

%Gel.  0.1M.  0.01  M. 

0  0.037704  0.005011 

1  0.033695  0.002413 

2  0.030608  0.000948 

3  0.027516  0.000755 

4  0.02423  0.000686 
10  0.009907  0.000462 
15  0.003987  0.000349 
20  0.002800  0.000233 

The  effect  of  the  gelatin  on  the  conductivity  of  the  0. 1  M  and  0. 01  M 
sulfuric  acid  solutions  is  also  shown  by  the  curves  in  Figs.  6  and  7.  The 
conductivities  are  plotted  as  ordinates  and  the  concentrations  of  gelatin 
as  abscissas.  These  curves  show  that  the  gelatin  produces  a  greater 
relative  change  in  the  conductivity  of  the  0.01  M  sulfuric  acid  solution 
than  in  the  conductivity  of  the  0. 1  M  solution.  It  should  be  recalled  that 
in  the  concentration-cell  measurements,  recorded  in  Table  IX,  the  gelatin 
produced  a  much  greater  relative  change  in  the  hydrogen-ion  concentration 
of  the  0.01  M  solution  than  in  the  0. 1  M.  In  fact,  by  the  addition  of 
about  3  to  4%  of  gelatin,  the  concentration  of  the  0.01  M  solution  was 


25 

reduced  practically  to  zero.  From  Fig.  7  it  is  readily  seen  that  by  the 
addition  of  about  3%  of  gelatin  the  conductivity  has  been  reduced  almost 
to  zero.  This  indicates  that  not  only  is  the  hydrogen-ion  concentration 
reduced  by  the  addition  of  gelatin  but  that  sulfuric  acid  is  removed  as 
a  whole. 


0.036 
0.034 
0-032 
0  030 
O.O28 
0.026 
0.024 
O.O22 
0.020 
00/8 
O.O/6 
O.OI4 
0.012 
O.OIO 
OOO8 
O006 

O  OO4 
O.O02 
O.OOO 

\ 

\ 

\ 

•  \ 

- 

\ 

\ 

fc 

\ 

\ 

fc 

1 

\ 

l 

\ 

\ 

/ 

7£ffC£-/V 

T  GIL* 

T/NE 

^—  < 

2     4     6     8     /O  /2  /4    /&     f8  2O 

Fig.  6. — Conductivity-gelatin  curve 
for  o.i  M  H2SO4. 


0.0026 


0.0000 


PER  ClNTGfLATlNE 


20 


02      4     6      8     /O    /2    /4    J6     /6 

Fig.  7. — Conductivity-gelatin  curve 
for  o.oi  M  H2SO4. 


Several  calculations  were  made  involving  the  conductivity  data  and 
potential  data  in  an  effort  to  determine  whether  the  gelatin  produced  an 
actual  change  in  the  mobility  of  the  ions,  but  it  was  impossible  to  conclude 
from  these  calculations  whether  the  effects  obtained  were  due  to  concentra- 
tion changes  alone  or  to  concentration  changes  together  with  changes  in 
mobility  or  the  presence  of  new  ions. 

Two  explanations  have  been  offered  to  account  for  the  action  of  gelatin, 

one  of  which  assumes  that  the  ions  of  the  acid  are  "absorbed"  by  the  gelatin, 

and  the  other  that  a  highly  dissociable  chemical  compound  is  formed. 

Supporters  of  the  first  theory  are  H.  G.  Bennett11  and  A.  Mutscheller;10 

11  Bennett,  /.  Am.  Leather  Chem.  Assoc.,  13,  270  (1918). 


26 

and  favoring  the  second  theory  are  H.  R  Procter,12  H.  R.  Procter  and  J.  A. 
Wilson,13  J.  Loeb,14  and  W.  O.  Fenn.15 

It  has  been  shown  in  this  investigation  that  some  of  the  properties  of 
sulfuric  acid  are  altered  by  the  presence  of  gelatin.  A  summary  of  the  data 
obtained  in  the  work  on  its  influence  on  the  transference  number  of  the 
anion  of  sulfuric  acid  is  contained  in  Table  VIII.  It  may  be  observed  that 
the  boundary  potential  (EB)  is  reduced  from  +0 . 02906  to  -  0 . 00006.  Cor- 
responding to  this  decrease  in  boundary  potential,  there  is  an  increase  in  the 
potential  of  the  hydrogen  concentration  cell  (EH)  from  0. 01136  to  0. 04155 
and  a  decrease  in  the  potential  of  the  sulfate  concentration  cell  (ESOt) 
from  0.04918  to  0.02068.  There  is  an  apparent  increase  in  the  trans- 
ference number  of  the  anion  from  0.187  to  0.685.  Any  factor  which 
would  increase  the  numerical  value  of  EH  and  decrease  ESOt  would 
give  the  observed  effect  of  a  decrease  in  the  boundary  potential  and  an  in- 
crease in  the  transference  number  of  the  anion.  This  factor  was  at  first 
believed  to  be  the  result  of  changes  in  concentration  which  are  recorded 
in  Table  IX,  due  to  the  presence  of  the  gelatin.  A  careful  consideration 
of  the  boundary  potentials  Ex,  EB,  and  Ez  which  result  from  these  changes 
in  concentration  leads,  to  the  conclusion  that  they  should  neutralize  each 
other.  The  data  in  Table  XI  show  this  to  be  the  fact.  Therefore  this 
effect  was  not  due  to  the  concentration  changes  brought  about  by  the 
introduction  of  the  gelatin.  This  led  to  the  conclusion  that  the  observed 
changes  in  the  potentials  of  the  concentrations  cells  resulted  from  a  change 
in  the  boundary  potentials.  This  decrease  in  the  boundary  potential 
could  be  produced  by  any  one  of  three  factors.  An  actual  change  in  the 
transference  numbers;  a  decrease  in  the  concentration  of  the  0.1  M  so- 
lution such  that  it  was  less  than  the  0.01  M  solution;  or  by  a  change 
in  the  kind  of  ions  present.  Since  the  second  of  these  factors  is  eliminated 
by  the  data  recorded  in  Table  IX,  which  shows  that  such  concentration 
changes  are  impossible,  it  appears  that  the  decrease  in  boundary  potential 
must  be  due  to  the  other  factors. 

As  there  is  a  possibility  that  a  chemical  compound  which  ionizes  is 
formed,  the  facts  are  considered  also  from  this  point  of  view.  If  such  is 
the  case  there  should  be  a  fairly  close  relation  between  the  amount  of 
gelatin  added  and  the  amount  of  acid  removed.  This  would  explain 
the  decrease  in  hydrogen-ion  concentration  and  decrease  in  conductivity 
observed.  If  such  a  reaction  occurs  new  compounds  are  formed  and  some 
of  the  hydrogen  ions  are  replaced  by  complex  gelatin  ions  which  results 
in  the  increase  in  the  transference  number  of  the  anion  as  observed.  No 

12  Procter,  /.  Chem.  Soc.,  100,  342-3  (1911);  105,  313  (1914). 

13  Procter  and  Wilson,  ibid.,  109, 307  (1916). 

"  Loeb,  /.  Gen.  Physiol.  1, 39-60,  237-54  (1918) ;  2, 363-85,  483-504,  559-80  (1919) . 
15  Fenn,  /.  Biol.  Chem.,  33,  279-94,  439-51  (1918);  34,  141-60,  415-28  (1918). 


27 

data  were  obtained  from  which  the  exact  amount  of  sulfuric  acid  removed 
by  a  definite  weight  of  gelatin  could  be  determined. 

From  the  curve  for  the  conductivity  of  the  0.1  M  sulfuric  acid  solution, 
Fig.  6,  it  appears  that  the  conductivity  of  the  solution  is  reduced  a  definite 
amount  for  each  additional  per  cent  of  gelatin.  The  addition  of  the  first 
per  cent  of  gelatin  in  the  0.01  M  solution  also  produces  about  the  same 
reduction  in  conductivity.  This  indicates  that  a  definite  quantity  of 
gelatin  removes  a  definite  amount  of  sulfuric  acid  from  the  solutions. 
If  the  compound  formed  dissociates,  and  some  evidence  has  been  obtained 
from  other  sources  that  it  does  then  the  conductivity  curves  will  tend  to 
flatten  at  the  higher  concentrations  of  gelatin.  Loeb14  has  been  led  to  be- 
lieve that  in  acid  solutions  gelatin  reacts  to  form  gelatin  salts  of  the  acid 
and  in  the  case  of  sulfuric  acid  he  states  that  the  gelatin  sulf ate  formed  has 
the  composition  represented  by  the  formula  gel4(SO4)2.  The  dissociation 
of  such  a  salt  would  result  in  the  formation  of  a  slowly  moving  complex 
colloidal  gelatin  cation  and  a  sulf  ate  anion.  The  transference  number 
of  the  anion  of  such  a  compound  would  be  greater  than  that  of  the  cation. 
This  conforms  to  the  observed  facts.  Furthermore,  such  a  compound 
would  show  some  conductivity,  so  that  for  the  higher  concentrations  of 
gelatin  the  decrease  in  conductivity  would  no  longer  be  proportional  to 
the  gelatin  added.  This  is  borne  out  by  the  flattening  of  the  conductivity 
curves  at  the  higher  concentrations  of  gelatin.  It  should  be  pointed  out 
that  the  sharp  bend  in  the  conductivity  curve  of  the  0.01  M  solution, 
Fig.  7,  occurs  at  about  the  same  concentration  as  a  similar  bend  in  the  gela- 
tin transference-number  curve,  Fig.  4;  furthermore  it  is  shown  from  the 
gelatin  concentration  cells,  Table  IX,  that  the  sulfuric  acid  in  0. 01  M  solu- 
tion is  practically  all  removed  at  this  same  concentration  of  gelatin. 

These  facts  indicate  that  sulfuric  acid  as  such  is  removed  by  the  addition 
of  gelatin  to  the  solution.     Accordingly  the  apparent  change  in  transference 
numbers  is  due  not  to  an  actual  change  in  the  velocity  of  the  H+  and  SO* 
ions,  but  to  the  presence  of  new  ions  in  the  solution  resulting  from  the  dis- 
sociation of  the  gelatin — sulf  ate  compound. 

It  is  the  opinion  of  the  author  that  the  aqtion  of  gelatin  and  sulfuric 
acid  results  in  the  formation  of  a  single  dissociable  product  in  which  the 
H+  ion  of  the  acid  loses  its  identity.  It  is  further  believed  that  in  the 
presence  of  a  base  a  similar  product  would  result  in  which  the  identity 
of  the  OH~  ion  would  be  lost  and  that  in  the  presence  of  a  neutral  salt 
solution  no  similar  action  would  result.  At  the  present  time  investigations 
are  being  conducted  by  the  author  to  confirm  this  hypothesis. 

Summary. 

1.  A  method  has  been  described  for  the  determination  of  the  trans- 
ference numbers  of  a  uni-bivalent  electrolyte  by  the  measurement  of  the 
potentials  of  concentration  cells. 


28 

2.  The  transference  number  of  the  anion  of  sulfuric  acid  for  concentra- 
tions between  0.1  M  and  0.01  M  has  been  measured  and  found  to  be 
0.1868  ±.7  at  25°. 

3.  It  has  been  shown  that  dissociation  values  determined  from  freezing- 
point  data  are  more  satisfactory  for  calculating  the  potentials  of  concen- 
tration cells  than  those  obtained  from  conductivity  data. 

4.  A  correction  to  the  formula  for  the  potential  of  a  concentration  cell 
has  been  developed  which  takes  into  account  the  undissociated  part  of 
the  acid. 

5.  It  has  been  shown  that  the  concentration-cell  method  is  entirely 
satisfactory  for  the  determination  of  the  transference  numbers  of  sulfuric 
acid. 

6.  The  effective  concentration  of  0.1  M  and  0.01  M  sulfuric  acid 
solutions  has  been  found  to  be  reduced  by  the  addition  of  gelatin. 

7.  The  transference  numbers  of  0.1  M  and  0.01  M  sulfuric  acid  so- 
lutions have  been  found  to  be  altered  by  the  presence  of  gelatin. 

8.  The  conductivities  of  sulfuric  acid  solutions  have  been  found  to  be 
reduced  by  the  presence  of  gelatin. 

9.  An  hypothesis  has  been  offered  to  account  for  the  action  of  gelatin 
in  the  presence  of  electrolytes. 


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